IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v350y2019icp163-169.html
   My bibliography  Save this article

Upper bound on the sum of powers of the degrees of graphs with few crossings per edge

Author

Listed:
  • Zhang, Xin

Abstract

A graph is q-planar if it can be drawn in the plane so that each edge is crossed by at most q other edges. For fixed integers q ≥ 1 and k ≥ 2, it is proven that 2(n−1)k+o(n) is an asymptotically tight upper bound on the sum of the k-th powers of the degrees of any simple q-planar graph with order n. As a result, an open problem listed at the end of the paper J. Czap, J. Harant, D. Hudák, Discrete Appl. Math. 165 (2014) 146–151 is solved.

Suggested Citation

  • Zhang, Xin, 2019. "Upper bound on the sum of powers of the degrees of graphs with few crossings per edge," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 163-169.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:163-169
    DOI: 10.1016/j.amc.2019.01.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319300104
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.01.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Su, Guifu & Tu, Jianhua & Das, Kinkar Ch., 2015. "Graphs with fixed number of pendent vertices and minimal Zeroth-order general Randić index," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 705-710.
    2. Shi, Yongtang, 2015. "Note on two generalizations of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1019-1025.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hua, Hongbo & Das, Kinkar Ch., 2016. "On the Wiener polarity index of graphs," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 162-167.
    2. Cui, Qing & Zhong, Lingping, 2017. "The general Randić index of trees with given number of pendent vertices," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 111-121.
    3. Das, Kinkar Ch., 2016. "On the Graovac–Ghorbani index of graphs," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 353-360.
    4. Lan, Yongxin & Li, Tao & Wang, Hua & Xia, Chengyi, 2019. "A note on extremal trees with degree conditions," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 70-79.
    5. Su, Guifu & Tu, Jianhua & Das, Kinkar Ch., 2015. "Graphs with fixed number of pendent vertices and minimal Zeroth-order general Randić index," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 705-710.
    6. Du, Zhibin, 2017. "Further results regarding the sum of domination number and average eccentricity," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 299-309.
    7. Ali, Akbar & Raza, Zahid & Bhatti, Akhlaq Ahmad, 2016. "Bond incident degree (BID) indices of polyomino chains: A unified approach," Applied Mathematics and Computation, Elsevier, vol. 287, pages 28-37.
    8. Das, Kinkar Ch. & Dehmer, Matthias, 2016. "Comparison between the zeroth-order Randić index and the sum-connectivity index," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 585-589.
    9. Wang, Ligong & Wang, Qi & Huo, Bofeng, 2016. "Integral trees with diameter four," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 53-64.
    10. Li, Fengwei & Ye, Qingfang & Sun, Yuefang, 2017. "On edge-rupture degree of graphs," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 282-293.
    11. Ma, Yuede & Cao, Shujuan & Shi, Yongtang & Dehmer, Matthias & Xia, Chengyi, 2019. "Nordhaus–Gaddum type results for graph irregularities," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 268-272.
    12. Fang Gao & Xiaoxin Li & Kai Zhou & Jia-Bao Liu, 2018. "The Extremal Graphs of Some Topological Indices with Given Vertex k -Partiteness," Mathematics, MDPI, vol. 6(11), pages 1-11, November.
    13. Nadeem, Muhammad Faisal & Zafar, Sohail & Zahid, Zohaib, 2016. "On topological properties of the line graphs of subdivision graphs of certain nanostructures," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 125-130.
    14. Fei, Junqi & Tu, Jianhua, 2018. "Complete characterization of bicyclic graphs with the maximum and second-maximum degree Kirchhoff index," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 118-124.
    15. Ma, Gang & Bian, Qiuju & Wang, Jianfeng, 2019. "The weighted vertex PI index of (n,m)-graphs with given diameter," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 329-337.
    16. Milovanović, E.I. & Milovanović, I.Ž. & Dolićanin, E.Ć. & Glogić, E., 2016. "A note on the first reformulated Zagreb index," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 16-20.
    17. Goubko, Mikhail, 2018. "Maximizing Wiener index for trees with given vertex weight and degree sequences," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 102-114.
    18. Yu, Guihai & Qu, Hui, 2015. "Hermitian Laplacian matrix and positive of mixed graphs," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 70-76.
    19. Borovićanin, Bojana & Furtula, Boris, 2016. "On extremal Zagreb indices of trees with given domination number," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 208-218.
    20. Li, Fengwei & Broersma, Hajo & Rada, Juan & Sun, Yuefang, 2018. "Extremal benzenoid systems for two modified versions of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 14-24.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:163-169. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.